Strong Convergence Theorem for Walsh–Kaczmarz–Fejér Means

Abstract

As main result we prove that Fejér means of Walsh–Kaczmarz–Fourier series are uniformly bounded operators from the Hardy martingale space \(\ H_{p}\) to the Hardy martingale space \(H_{p}\) for \( 0<p\le 1/2\).

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Correspondence to George Tephnadze.

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Research supported by projects TÁMOP-4.2.2.A-11/1/KONV-2012-0051, GINOP-2.2.1-15-2017-00055 and by Shota Rustaveli National Science Foundation grant no. FR-19-676.

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Gogolashvili, N., Nagy, K. & Tephnadze, G. Strong Convergence Theorem for Walsh–Kaczmarz–Fejér Means. Mediterr. J. Math. 18, 37 (2021). https://doi.org/10.1007/s00009-020-01682-5

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Keywords

  • Walsh–Kaczmarz system
  • Fejér means
  • maximal operator
  • strong convergence
  • martingale Hardy space

Mathematics Subject Classification

  • 42C10